Game-perfect digraphs

Stephan Andres ()

Mathematical Methods of Operations Research, 2012, vol. 76, issue 3, 341 pages

Abstract: In the A-coloring game, two players, Alice and Bob, color uncolored vertices of a given uncolored digraph D with colors from a given color set C, so that, at any time a vertex is colored, its color has to be different from the colors of its previously colored in-neighbors. Alice begins. The players move alternately, where a move of Bob consists in coloring a vertex, and a move of Alice in coloring a vertex or missing the turn. The game ends when Bob is unable to move. Alice wins if every vertex is colored at the end, otherwise Bob wins. This game is a variant of a graph coloring game proposed by Bodlaender (Int J Found Comput Sci 2:133–147, 1991 ). The A-game chromatic number of D is the smallest cardinality of a color set C, so that Alice has a winning strategy for the game played on D with C. A digraph is A-perfect if, for any induced subdigraph H of D, the A-game chromatic number of H equals the size of the largest symmetric clique of H. We characterize some basic classes of A-perfect digraphs, in particular all A-perfect semiorientations of paths and cycles. This gives us, as corollaries, similar results for other games, in particular concerning the digraph version of the usual game chromatic number. Copyright Springer-Verlag 2012

Keywords: Dichromatic number; Digraph; Game chromatic number; Game-perfectness; Perfect graph; Quasi coloring (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s00186-012-0401-x

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